/*
 * Copyright (c) 2003, the JUNG Project and the Regents of the University 
 * of California
 * All rights reserved.
 *
 * This software is open-source under the BSD license; see either
 * "license.txt" or
 * http://jung.sourceforge.net/license.txt for a description.
 * 
 * Created on Feb 18, 2004
 */
package edu.uci.ics.jung.algorithms.util;

import java.util.Collection;
import java.util.Iterator;

/**
 * A utility class for calculating properties of discrete distributions.
 * Generally, these distributions are represented as arrays of
 * <code>double</code> values, which are assumed to be normalized such that the
 * entries in a single array sum to 1.
 * 
 * @author Joshua O'Madadhain
 */
public class DiscreteDistribution {

	/**
	 * Returns the Kullback-Leibler divergence between the two specified
	 * distributions, which must have the same number of elements. This is
	 * defined as the sum over all <code>i</code> of
	 * <code>dist[i] * Math.log(dist[i] / reference[i])</code>. Note that this
	 * value is not symmetric; see <code>symmetricKL</code> for a symmetric
	 * variant.
	 * 
	 * @see #symmetricKL(double[], double[])
	 */
	public static double KullbackLeibler(double[] dist, double[] reference) {
		double distance = 0;

		checkLengths(dist, reference);

		for (int i = 0; i < dist.length; i++) {
			if (dist[i] > 0 && reference[i] > 0) {
				distance += dist[i] * Math.log(dist[i] / reference[i]);
			}
		}
		return distance;
	}

	/**
	 * Returns
	 * <code>KullbackLeibler(dist, reference) + KullbackLeibler(reference, dist)</code>
	 * .
	 * 
	 * @see #KullbackLeibler(double[], double[])
	 */
	public static double symmetricKL(double[] dist, double[] reference) {
		return KullbackLeibler(dist, reference)
				+ KullbackLeibler(reference, dist);
	}

	/**
	 * Returns the squared difference between the two specified distributions,
	 * which must have the same number of elements. This is defined as the sum
	 * over all <code>i</code> of the square of
	 * <code>(dist[i] - reference[i])</code>.
	 */
	public static double squaredError(double[] dist, double[] reference) {
		double error = 0;

		checkLengths(dist, reference);

		for (int i = 0; i < dist.length; i++) {
			double difference = dist[i] - reference[i];
			error += difference * difference;
		}
		return error;
	}

	/**
	 * Returns the cosine distance between the two specified distributions,
	 * which must have the same number of elements. The distributions are
	 * treated as vectors in <code>dist.length</code>-dimensional space. Given
	 * the following definitions
	 * <ul>
	 * <li><code>v</code> = the sum over all <code>i</code> of
	 * <code>dist[i] * dist[i]</code>
	 * <li><code>w</code> = the sum over all <code>i</code> of
	 * <code>reference[i] * reference[i]</code>
	 * <li><code>vw</code> = the sum over all <code>i</code> of
	 * <code>dist[i] * reference[i]</code>
	 * </ul>
	 * the value returned is defined as
	 * <code>vw / (Math.sqrt(v) * Math.sqrt(w))</code>.
	 */
	public static double cosine(double[] dist, double[] reference) {
		double v_prod = 0; // dot product x*x
		double w_prod = 0; // dot product y*y
		double vw_prod = 0; // dot product x*y

		checkLengths(dist, reference);

		for (int i = 0; i < dist.length; i++) {
			vw_prod += dist[i] * reference[i];
			v_prod += dist[i] * dist[i];
			w_prod += reference[i] * reference[i];
		}
		// cosine distance between v and w
		return vw_prod / (Math.sqrt(v_prod) * Math.sqrt(w_prod));
	}

	/**
	 * Returns the entropy of this distribution. High entropy indicates that the
	 * distribution is close to uniform; low entropy indicates that the
	 * distribution is close to a Dirac delta (i.e., if the probability mass is
	 * concentrated at a single point, this method returns 0). Entropy is
	 * defined as the sum over all <code>i</code> of
	 * <code>-(dist[i] * Math.log(dist[i]))</code>
	 */
	public static double entropy(double[] dist) {
		double total = 0;

		for (int i = 0; i < dist.length; i++) {
			if (dist[i] > 0) {
				total += dist[i] * Math.log(dist[i]);
			}
		}
		return -total;
	}

	/**
	 * Throws an <code>IllegalArgumentException</code> if the two arrays are not
	 * of the same length.
	 */
	protected static void checkLengths(double[] dist, double[] reference) {
		if (dist.length != reference.length) {
			throw new IllegalArgumentException(
					"Arrays must be of the same length");
		}
	}

	/**
	 * Normalizes, with Lagrangian smoothing, the specified <code>double</code>
	 * array, so that the values sum to 1 (i.e., can be treated as
	 * probabilities). The effect of the Lagrangian smoothing is to ensure that
	 * all entries are nonzero; effectively, a value of <code>alpha</code> is
	 * added to each entry in the original array prior to normalization.
	 * 
	 * @param counts
	 * @param alpha
	 */
	public static void normalize(double[] counts, double alpha) {
		double total_count = 0;

		for (int i = 0; i < counts.length; i++) {
			total_count += counts[i];
		}

		for (int i = 0; i < counts.length; i++) {
			counts[i] = (counts[i] + alpha)
					/ (total_count + counts.length * alpha);
		}
	}

	/**
	 * Returns the mean of the specified <code>Collection</code> of
	 * distributions, which are assumed to be normalized arrays of
	 * <code>double</code> values.
	 * 
	 * @see #mean(double[][])
	 */
	public static double[] mean(Collection<double[]> distributions) {
		if (distributions.isEmpty()) {
			throw new IllegalArgumentException(
					"Distribution collection must be non-empty");
		}
		Iterator<double[]> iter = distributions.iterator();
		double[] first = iter.next();
		double[][] d_array = new double[distributions.size()][first.length];
		d_array[0] = first;
		for (int i = 1; i < d_array.length; i++) {
			d_array[i] = iter.next();
		}

		return mean(d_array);
	}

	/**
	 * Returns the mean of the specified array of distributions, represented as
	 * normalized arrays of <code>double</code> values. Will throw an
	 * "index out of bounds" exception if the distribution arrays are not all of
	 * the same length.
	 */
	public static double[] mean(double[][] distributions) {
		double[] d_mean = new double[distributions[0].length];
		for (int j = 0; j < d_mean.length; j++) {
			d_mean[j] = 0;
		}

		for (int i = 0; i < distributions.length; i++) {
			for (int j = 0; j < d_mean.length; j++) {
				d_mean[j] += distributions[i][j] / distributions.length;
			}
		}

		return d_mean;
	}

}